For u; v 2 V, define d.u; v/ D ku vk.(a) Show that d is a metric on V.(b) Show that if V
Chapter 6, Problem 29(choose chapter or problem)
For u; v 2 V, define d.u; v/ D ku vk.(a) Show that d is a metric on V.(b) Show that if V is finite-dimensional, then d is a complete metricon V (meaning that every Cauchy sequence converges).(c) Show that every finite-dimensional subspace of V is a closedsubset of V (with respect to the metric d).
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